Antenna selection (AS) is a signal processing technique that activates a selected subset of available antennas in multi-antenna systems, based on which a performance-hardware tradeoff can be achieved by reducing the number of costly radio-frequency (RF) chains. The biggest challenge of AS is the combinatorial complexity that arises from the classic K-out-of-N problem, which makes it more challenging for massive MIMO systems equipped with large-scale antenna arrays. In addition, for massive MIMO systems with limited RF chains, the amount of radio resources dedicated to channel state information (CSI) measurement will increase tremendously, which may highly degrade the overall performance of AS. In this paper, we consider the transmit AS problem in time division duplexing (TDD) massive MIMO systems, where K out of N transmit antennas are selected to maximize the total throughput of M single-antenna users in the downlink. We propose an online learning scheme and introduce Thompson sampling techniques to update the set of active antennas with partial CSI. The idea behind is to find an efficient tradeoff between the exploitation of high-performance antennas and the exploration of antennas with uncertain CSI with low complexity. Our proposed scheme is validated by using COST 2100 channel model, and simulation results show that it greatly outperforms the conventional power-based and convex relaxation based schemes, in terms of the total downlink throughput.